Theorems · Theorem · group theory
Subsemigroup.coe_iInf
∀ {M : Type u_1} [inst : Mul M] {ι : Sort u_3} {S : ι → Subsemigroup M}, ↑(⨅ i, S i) = ⋂ i, ↑(S i)- Defined in
- Mathlib.Algebra.Group.Subsemigroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- iInfstatement · cited by 1,690
- Set.iInterstatement and proof · cited by 1,084
- Subsemigroupstatement and proof · cited by 323
- Set.biInter_rangeproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Subsemigroup.map_iInfproof · cited by 0